SOLUTION: I have a formula by Huebsher used in engineering duct design. It calculates the equivalent diameter of a round duct using length major (width) and length minor (height) of a rectan

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Question 1103698: I have a formula by Huebsher used in engineering duct design. It calculates the equivalent diameter of a round duct using length major (width) and length minor (height) of a rectangular duct. I need to solve this equation for the length major (width) of the rectangular duct because height and equivalent diameter of a round duct will be already known. The formula is d=1.30%28ab%29%5E0.625+%2F%28a%2Bb%29%5E0.25 where d=round duct diameter, b=length minor (duct height) and a=length major (duct width) I need to solve for a (a=???) I am making an Excel calculator for my duct sizing and the formula is solved for the wrong variable for my use.
Found 2 solutions by Alan3354, math_helper:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I have a formula by Huebsher used in engineering duct design. It calculates the equivalent diameter of a round duct using length major (width) and length minor (height) of a rectangular duct. I need to solve this equation for the length major (width) of the rectangular duct because height and equivalent diameter of a round duct will be already known. The formula is d=1.30%28ab%29%5E0.625+%2F%28a%2Bb%29%5E0.25 where d=round duct diameter, b=length minor (duct height) and a=length major (duct width) I need to solve for a (a=???)
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That's a mess.
I would do it from scratch.
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Area of rectangle = a*b
Area of circle = pi*d^2/4
For equal areas: a*b = pi*d^2/4
a+=+pi%2Ad%5E2%2F%284b%29
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I looked up Huebner, and it apparently takes into account other factors besides area.
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d=1.30%28ab%29%5E0.625+%2F%28a%2Bb%29%5E0.25
d%5E4+=+1.3%5E4%28ab%29%5E2.5+%2F%28a%2Bb%29
d%5E4%2A%28a%2Bb%29+=+1.3%5E4%28ab%29%5E2.5
%28d%5E4%2Aa+%2B+d%5E4%2Ab%29+=+1.3%5E4%2A%28a%5E2.5%2Ab%5E2.5%29
a%2Ad%5E4+-+a%5E2.5%2A1.3%5E4%2Ab%5E2.5+-+b%2Ad%5E4+=+0
At this point I would try an Excel sheet.



Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
While I agree with the other tutor's mathematics, if the poster wants to use this in the real world, then there is this caveat: the Huebsher formula may (read: is very likely) taking into account certain physical attributes, such as frictional losses for the air flow for the different physical geometries.